Simplify the following expression: $\sqrt{150}+\sqrt{6}-\sqrt{24}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{150}+\sqrt{6}-\sqrt{24}$ $= \sqrt{25 \cdot 6}+\sqrt{6}-\sqrt{4 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{6}+\sqrt{6}-\sqrt{4} \cdot \sqrt{6}$ $= 5\sqrt{6}+\sqrt{6}-2\sqrt{6}$ Finally, simplify by combining the terms. $= ( 5 + 1 - 2 )\sqrt{6} = 4\sqrt{6}$